When accepting what the Bible (or any other text) has to say, it isn't an all-or-nothing deal. It could be that a book makes 10 claims, and only 7 of them are correct. How would we know which are true, and which are false, outside of independently validating each one?

The same applies to the Bible.

Clearly, Egypt existed, and so did some other cities mentioned in the Bible. Thus, we'll believe those specific claims. When it comes to the notion that a person was the son of a god, and performed miracles, those claims earn no credibility simply because they're in the same book (the Bible) as other claims that happen to be true.

Those miracle/god claims would need to be independently validated. The parts of the Bible we don't believe, we don't believe due to insufficient evidence.

So it's not so much that we don't "believe the Bible", as much as the Bible has ten thousand claims, and only a small portion of them have been sufficiently demonstrated. The factual assertions that do align to reality (assuming we're not talking about passages like philosophical parables) are mundane and trivial.